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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On subgroups of the multiplicative group of skew fields


Author: A. Lichtman
Journal: Proc. Amer. Math. Soc. 63 (1977), 15-16
MSC: Primary 20H20; Secondary 16A18
DOI: https://doi.org/10.1090/S0002-9939-1977-0447432-0
MathSciNet review: 0447432
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Abstract: We give an example of a skew field D for which the multiplicative group $ {D^ \ast }$ of D contains a finitely generated subgroup which satisfies a nontrivial identity and has no solvable normal subgroup of finite index. It gives a negative answer to a question of S. Bachmuth.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0447432-0
Keywords: Multiplicative group of division ring, group ring
Article copyright: © Copyright 1977 American Mathematical Society